Lp-saturation of some modified Bernstein operators

On simultaneous approximation for some modified Bernstein-type operators

for n ≥ α, where α, β are integers satisfying α ≥ β ≥ 0 and In ⊆ {0,1,2, . . . ,n} is a certain index set. For α = β = 0, In = {0}, this definition reduces to the BernsteinDurrmeyer operators, which were first studied by Derriennic [3]. Also if α = β = 1, In = {0}, we obtain the recently introduced sequence of Gupta and Maheshwari [4], that is, Mn,1,1(f ,x)≡ Pn(f ,x) which is defined as Pn(f ,x...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Lp-INVERSE THEOREM FOR MODIFIED BETA OPERATORS

and B(v+1,n) being the beta function (see, e.g., [3]). It is easily verified that the operators Bn are linear positive operators. Also, Bn(1,x) = 1. It turns out that the order of approximation for the operators (1.1) is at best O(n−1) howsoever smooth the function may be. With the aim of improving the order of approximation, we have to slack the positive condition of these operators for which ...

Statistical approximation of modified Schurer-type q-Bernstein Kantorovich operators

New modified Schurer-type q-Bernstein Kantorovich operators are introduced. The local theorem and statistical Korovkin-type approximation properties of these operators are investigated. Furthermore, the rate of approximation is examined in terms of the modulus of continuity and the elements of Lipschitz class functions.

Modified (p,q)-Bernstein-Schurer operators and their approximation properties